A344905 Decimal expansion of the solution to x^x = sqrt(2).

1, 3, 0, 4, 3, 5, 1, 1, 7, 8, 9, 0, 1, 0, 3, 6, 5, 3, 3, 6, 4, 7, 2, 0, 1, 2, 3, 1, 4, 8, 6, 2, 3, 4, 0, 7, 5, 0, 3, 5, 5, 3, 3, 8, 2, 9, 9, 8, 9, 0, 2, 3, 1, 7, 9, 8, 1, 7, 3, 3, 2, 0, 9, 5, 6, 8, 8, 9, 1, 5, 0, 9, 3, 2, 8, 7, 5, 7, 1, 2, 2, 1, 0, 0, 0, 4, 8

Offset: 1

Author

Christoph B. Kassir, Jun 01 2021

Keywords

• cons
• nonn

Examples

			1.304351178901036533647201231486234...
		

Crossrefs

Cf. A030798, A073084.

Programs

Mathematica

RealDigits[Log[Sqrt[2]]/ProductLog[Log[Sqrt[2]]], 10, 100][[1]] (* Amiram Eldar, Jun 02 2021 *)
RealDigits[x/.FindRoot[x^x==Sqrt[2],{x,1},WorkingPrecision-> 120],10,120][[1]] (* Harvey P. Dale, Jun 18 2021 *)

PARI

solve(x=1,2,x^x-sqrt(2)) \\ Hugo Pfoertner, Jun 02 2021

Formula

Equals log(2)/(2*LambertW(log(2)/2)). - Alois P. Heinz, Jun 02 2021

Equals 1/A073084. - Jason Bard, Aug 20 2025